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Multivariate measures of skewness for the skew-normal distribution

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
104
Issue
1
Identifiers
DOI: 10.1016/j.jmva.2011.06.017
Keywords
  • Multivariate Skewness
  • Skew-Normal Distributions
  • Mardia Measure Of Skewness
  • Malkovich–Afifi Measure
  • Isogai Measure
  • Srivastava Measure
  • Móri
  • Rohatgi And Székely Measure
  • Kollo Measure
  • Balakrishnan–Brito–Quiroz Measure
  • Song Measure Of Shape

Abstract

Abstract The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9], Isogai (1982) [17], Srivastava (1984) [15], Song (2001) [14], Móri et al. (1993) [11], Balakrishnan et al. (2007) [3] and Kollo (2008) [7] measures of skewness. The exact expressions of all measures of skewness, except for Song’s, are derived for the family of skew-normal distributions, while Song’s measure of shape is approximated by the use of delta method. The behavior of these measures, their similarities and differences, possible interpretations, and their practical use in testing for multivariate normal are studied by evaluating their power in the case of some specific members of the multivariate skew-normal family of distributions.

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